2016/11/07 by Mevlana Gemici, Danilo Jimenez Rezende, Gemici, Mevlana C. +3 · 7 citations
Computer Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1611.02304
openalex publication_date 2016/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as used in protein folding, robot limbs, gene-expression) and in general directional statistics. In spite of the multitude of algorithms available for density estimation in the Euclidean spaces Rn that scale to large n (e.g. normalizing flows, kernel methods and variational approximations), most of these methods are not immediately suitable for density estimation in more general Riemannian manifolds. We revisit techniques related to homeomorphisms from differential geometry for projecting densities to sub-manifolds and use it to generalize the idea of normalizing flows to more general Riemannian manifolds. The resulting algorithm is scalable, simple to implement and suitable for use with automatic differentiation. We demonstrate concrete examples of this method on the n-sphere Sn.